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Self-adjoint Extensions of Restrictions
We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator $S$ obtained by restricting the self-adjoint operator…
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A Krein-like Formula for Singular Perturbations of Self-Adjoint Operators and Applications
Abstract Given a self-adjoint operator A :  D ( A )⊆ H → H and a continuous linear operator τ :  D ( A )→ X with Range τ ′∩ H ′={0}, X a Banach space, we explicitly construct a family A τ Θ of…
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Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
Given the symmetric operator $A_N$ obtained by restricting the self-adjoint operator $A$ to $N$, a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple…
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On the spectral theory of Gesztesy–Šeba realizations of 1-D Dirac operators with point interactions on a discrete set
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On inverses of Krein's Q-functions
Let $A_{Q}$ be the self-adjoint operator defined by the $Q$-function $Q:z\mapsto Q_{z}$ through the Krein-like resolvent formula $$(-A_{Q}+z)^{-1}= (-A_{0}+z)^{-1}+G_{z}WQ_{z}^{-1}VG_{\bar…
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Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators
Given a symmetric, semi-bounded, second-order elliptic differential operator A on a bounded domain with C1,1 boundary, we provide a Kreĭn-type formula for the resolvent difference between its…
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Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
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Wave equations with concentrated nonlinearities
In this paper, we address the problem of wave dynamics in the presence of concentrated nonlinearities. Given a vector field V on an open subset of and a discrete set with n elements, we define a…
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Finite speed of propagation and local boundary conditions for wave equations with point interactions
We show that the boundary conditions entering in the definition of the self-adjoint operator Delta(A,B) describing the Laplacian plus afinite number of point interactions are local if and only if the…
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On the Self-Adjointness of H+A∗+A
Let $H:D(H)\subseteq{\mathscr F}\to{\mathscr F}$ be self-adjoint and let $A:D(H)\to{\mathscr F}$ (playing the role of the annihilator operator) be $H$-bounded. Assuming some additional hypotheses on…
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